3 Answers
3

"The Rishonim [end of Tractate
Pesachim] ask the following: 'Why
don't we count Sefirat HaOmer each
night twice [i.e., "today is the
second day," and "today is the first
day," etc.] due to the doubtful day?'

"HaRav Joseph B. Soloveitchik, zt"l,
heard a reason why we do not do so
from the Kovno Rav [see Devar
Avraham]: If a person counts twice due
to doubt, i.e., stating that it is
either the fourth day of the Omer or
the fifth day of the Omer, he will not
have fulfilled his mitzva at all
because a doubtful count is not
considered a count. Our Sages stated
in the first perek of Bava Metzia
regarding ma'aser behema that it must
be the tenth of every ten animals, and
not a doubtful tenth."

In conclusion, now that we have an
established calendar and our
celebration of two days Yom Tov is
only due to the minhag of our fathers,
as noted in the beginning of Tractate
Beitza, we count consecutive numbers
each night, starting from the second
night of Pesach until we have counted
seven complete weeks - to Shavuot

… because we shouldn't be so strict about it, since it's nothing but a remembrance to what was done when we had the bes hamikdash.

Another [reason] is that if we count one day ahead then we'll reach number 49 on Shavuos, which we'll therefore come to treat lightly. (Avudraham.)

He then offers a reason of his own. I'll quote it, but I don't understand it:

If we count twice in one day, then one will need to count "today is the second day" on the third day, and, in case the first day is the true [first day], he'll need to count "today is the third day" with a blessing on the third day. And likewise for every day.